What are the divisors of 5819?

1, 11, 23, 253, 529, 5819

There is a total of 6 positive divisors.
The sum of these divisors is 6636.
The arithmetic mean is 1106.

6 odd divisors

1, 11, 23, 253, 529, 5819

How to compute the divisors of 5819?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5819 by each of the numbers from 1 to 5819 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5819 / 1 = 5819 (the remainder is 0, so 1 is a divisor of 5819)
5819 / 2 = 2909.5 (the remainder is 1, so 2 is not a divisor of 5819)
5819 / 3 = 1939.6666666667 (the remainder is 2, so 3 is not a divisor of 5819)
...
5819 / 5818 = 1.0001718803713 (the remainder is 1, so 5818 is not a divisor of 5819)
5819 / 5819 = 1 (the remainder is 0, so 5819 is a divisor of 5819)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5819 (i.e. 76.282370178174). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5819 / 1 = 5819 (the remainder is 0, so 1 and 5819 are divisors of 5819)
5819 / 2 = 2909.5 (the remainder is 1, so 2 is not a divisor of 5819)
5819 / 3 = 1939.6666666667 (the remainder is 2, so 3 is not a divisor of 5819)
...
5819 / 75 = 77.586666666667 (the remainder is 44, so 75 is not a divisor of 5819)
5819 / 76 = 76.565789473684 (the remainder is 43, so 76 is not a divisor of 5819)